COMPLAS 2023

On the transition from diffusive to discrete crack topologies in crack phase-field model

  • Han, Jike (Tohoku University)
  • Shintaku, Yuichi (University of Tsukuba)
  • Moriguchi, Shuji (Tohoku University)
  • Terada, Kenjiro (Tohoku University)

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Fracture is one of the most crucial failure mechanisms in engineering fields. As well as the development of computer performance and failure/damage mechanics, numerical simulation methods for predicting fracture problems in more complex and larger geometries are required. In this trend, the crack phase-field (PF) model [1] is a promising candidate for predicting arbitrary crack initiation, propagation, and bifurcation. However, when implemented into a standard finite element program, the PF model encounters several issues that the continuum damage model usually faces. In particular, the severely damaged finite elements and mesh collapse cause the failure of Newton–Raphson computations. Also, the independent movements of multiple portions divided by crack are almost unable to be traced. In this study, a transition scheme from diffusive to discrete crack topologies [2] is presented. The transition scheme can trace an actual crack path as closely as possible and stably update its explicit crack surfaces even in a large deformation regime. The crack initiation, propagation, and bifurcation are determined from an energy minimization problem with respect to the displacement field and the crack phase-field, while the predicted path represented by a diffuse crack topology is replaced by a discrete path by applying the finite cover method. Accordingly, the entire braking process and the subsequent independent movements of multiple portions can be captured by one single numerical setup. Several representative numerical examples are presented to show the stable update from diffusive to discrete crack topologies intermittently during the course of a staggered iterative procedure in a single time step within the finite strain framework. [1] Wu et al., Advances in Applied Mechanics, 53, 2020:1-183. doi:10.1016/bs.aams.2019.08.001 [2] Han et al., Int J Numer Methods Eng., 2022. doi:10.1002/nme.7169